We present a novel interpretation of the thermodynamics of perfect fluid dark matter (PFDM) black hole based on Misner–Sharp energy and then investigate its evaporation behavior. We find that the ratio between dark sector initial density and black hole horizon radius significantly influences black hole evaporation behaviors. We demonstrate that the presence of the dark sector can significantly extend the lifetime of a black hole which is similar to the Reissner–Nordström case. Our work reformulates the thermodynamics of PFDM black holes and points out the existence of long-lived black holes in the presence of the dark sector.

A high Fe content easily produces Fe-rich phases with a harmful morphology, resulting in a huge detrimental effect on the properties and recycling ability of Al-Si alloys. Therefore, finding ways to effectively transform Fe-rich phases to form a beneficial phase or shape is of great significance. Accordingly, Al-Si-based alloys with Fe contents ranging from 0.1 wt.% to 2.0 wt.% were modified by different Mn additions. Moreover, experiments combined with simulations were utilized to comprehensively analyze the mechanism of Mn on the morphology and microstructural evolution of Fe-rich phases from different perspectives. The current findings determine that adding different Fe contents changes the phase-transition reactions in alloys. Without Mn, and by increasing the Fe content from 0.1 wt.% to 2.0 wt.%, the Fe-rich phases gradually convert from a skeleton-shaped α-Al₈Fe₂Si (<0.25 wt.%) to β-Al₉Fe₂Si₂ with a fibrous (0.5 wt.%), needle-like (1.0 wt.%) and plate-like shape without curvatures (2.0 wt.%). The maximum length and mean aspect ratio increase from 12.01 μm to 655.66 μm and from 1.96 to 84.05, while the mean curvature decreases from 8.66 × 10⁻² μm⁻¹ to 8.25 × 10⁻⁴ μm⁻¹. The addition of 0.35 wt.% Mn promotes a new Chinese-character and petal-shaped α-Al₁₅(FeMn)₃Si₂, with an atomic ratio of Fe and Mn of 1:1 when the Fe content is lower than 0.5 wt.%, while it transforms to β-Al₁₅(FeMn)₃Si₂ with an atomic ratio of 5:1, presenting as a refined plate-like shape with a certain curvature, as the Fe content increases to 2.0 wt.%. Mn alters the phase reactions and increases the threshold of the Fe content required for β-Al₁₅(FeMn)₃Si₂, limiting the formation and growth of them simultaneously in time and space. The enrichment of Mn atoms and solute diffusion at the growth front of β-Al₁₅(FeMn)₃Si₂, as well as the strong atomic-binding ability, can deflect the growth direction of β-Al₁₅(FeMn)₃Si₂ for it to have a certain curvature. Additionally, the enriched Mn atoms easily form α-Al₁₅(FeMn)₃Si₂ and cause the long β-Al₁₅(FeMn)₃Si₂ to be broken and refined to further reduce the damages caused to the alloy’s performance. Ultimately, the maximum length and mean aspect ratio can be effectively reduced to 46.2% and 42.0%, respectively, while the mean curvature can be noticeably increased by 3.27 times with the addition of Mn.

To elucidate the phase transformation behaviors for 38MnB5Nb ultra high-strength steel, the continuous cooling transformation (CCT) and time-temperature-transformation (TTT) curves were determined by the thermal expansion method with different cooling rates and isothermal temperatures after complete austenization. To be more accurate, the microstructure was observed and the hardness was tested. The results showed that the starting and ending transformation temperatures of austenite during heating are 748 °C and 805 °C, respectively. Bainite’s start temperature is between 540 °C and 550 °C, while martensite’s start temperature is about 310 °C. The critical cooling transformation rate is between 10 °C/s and 15 °C/s. The results showed that the microstructures are severely related to the cooling rate during the continuous cooling process and are related to isothermal temperatures during the isothermal process. The relationship between hardness and the microstructure was investigated and hardness is severely related to the microstructure. Based on the results of CCT curves compared with the conventional 22MnB5 hot stamping steel, the studied 38MnB5Nb steel is more beneficial for selective cooling processes.